Apps. and Interpretation for IBDP Maths Ebook 1 | Page 279

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Paper 1 – Unknown Probabilities with Given
Example
The random variable X has the following probability distribution.
x 2 4 6
P( X � x)
a b 0.25
(a)
Find the first equation connecting a and b , giving the answer in the form
pa �qb � r .
It is given that E( X ) � 3.4 .
[2]
(b)
Find the second equation connecting a and b , giving the answer in the form
pa �qb � r .
(c) Hence, write down the values of a and b .
[2]
[2]
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Solution
(a) P( X � 2) � P( X � 4) � P( X � 6) � 1
(A1) for correct formula
a�b�
0.25 � 1
a�b� 0.75
A1 N2
(b) E( X ) � 3.4
2a� 4 b� (6)(0.25) � 3.4
(A1) for correct formula
2a�4b� 1.9
A1 N2
(c) a � 0.55 , b � 0.2
A2 N2
[2]
[2]
[2]
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